A　numerical　study　is　performed　on　the　cool-down　behavior　and　thermal　stress　of　a　cryogenic　tank　during　the　saturated　hydrogen　gas　filling　process.　CFD　simulation　is　carried　out　to　obtain　the　flow　and　temperature　distributions　inside　the　tank　and　the　temperature　distribution　of　the　tank　wall　under　a　specific　filling　rate.　Then　the　flow　and　cooling　characteristics　of　the　tank　during　the　filling　process　are　analyzed.　The　thermal　stress　in　the　tank　wall　under　three　different　constraints　of　the　inlet　and　outlet　is　calculated　with　unidirectional　fluid-solid　coupling　method,　and　the　spatial　distribution　and　transient　behavior　of　the　thermal　stress　are　revealed.　In　addition,　the　rationality　of　applying　elastic　supports　to　the　inlet　and　outlet　is　demonstrated,　and　the　integrated　stress　in　the　tank　wall　is　calculated　with　the　pressure　variation　in　the　tank　taken　into　account.　Numerical　results　show　that　the　filling　process　can　be　divided　into　three　steps,　where　the　flow　and　temperature　distributions　inside　the　tank　are　governed　by　the　forced　convection　from　the　inlet　or　the　natural　convection　near　the　wall　in　the　first　and　second　steps,　and　by　both　of　them　in　the　third　step.　The　maximum　thermal　stress　appears　at　the　inlet　and　outlet　of　the　tank　under　any　of　the　three　constraints.　For　radial　elastic　support　on　the　inlet　and　outlet,　the　maximum　thermal　stress　increases　gradually　to　a　steady　value　and　takes　up　about　15%　of　the　maximum　integrated　stress　in　steady　state.